Let the tens digits of the number be x and the unit digit be y

3x = 2y - 2

3x - 2y = -2.......(i)

If the digits are interchanged, the tens digit becomes y, the unit digit becomes x.

Hence 2(10x + y) = 10y + x + 20

(20x + 2y) - (10y + x) = 20

19x - 8y = 20.....(ii)

Multiply eqn.(i) by 8 and eqn.(ii) by 2

24x - 16y = -16......(iii)

38x - 16y = 40........(iv)

eqn(iv) - eqn(iii)

14x = 56

x = 4

Sub. for x = 4 in eqn(i)

3(4) - 2y = -2

14 = 2y

y = 7

So the original number is 10(4) + 7 i.e. 10x + y
= 47